It is known how to write a quantum description of strings, cf. for instance, https://www.damtp.cam.ac.uk/user/tong/string.html.

Dark matter is just a form of matter, its particle content is, up to now, unknown, that's why it's possible to write many quantum field theories, that describe extensions of the Standard Model, the quantum field theory that describes the particles, that make up the known forms of matter. The problem is imagining the experiments that can distinguish between them. And if dark matter has only gravitational interactions, it just won't be possible to resolve its particle content-its equation of state is, already, known, but that doesn't imply anything about its particle content.

As long as dark energy can be described by the cosmological constant, its description is provided within the classical limit of the quantum theory of gravity.

So, while dark matter does have a straightforward quantum description-though, for the moment, only its classical effects are relevant and detectable, dark energy does not have, for the moment, a quantum description; however such a description is not required, since it isn't possible, yet, to probe, through measurements, the pre-inflationary epoch of our Universe, where such a description would be required.

Dark matter and dark energy are related to Quantum and cosmic world because the Fabriton particles are distributed in the structure of Atom to hold electrons whith atomic nuclei. The fabriton particles are available in the structure of stars and whole universe to make gravitation among celestial objects according to my published articles by Sabir Sadiq

Shreya Jaiswal > "Do dark energy and dark matter follow quantum theory?"

The answer is NO! "Dark energy and dark matter" or any other dark/black objects coming out of the mother of ALL DARKNESS, namely the "Big Bang" theory; do not follow any theory - quantum or non-quantum! Because all these arise from mainly two brain-cooked and fantasy axiomatic theories of the past centuries; which are unscientific and have no basis in objective reality! Please see the following copy of a dialogue in RG:

[Sergio Leal Ramirez added a reply August 24

Thank you for this profound and timely intervention. As a scholar deeply engaged in the epistemology and pedagogy of mathematics and physics, I find your critique not only philosophically rigorous but pedagogically urgent. You are absolutely correct: the two foundational theories you identify—Newton’s Law of Universal Gravitation and Einstein’s postulate of the constancy of the speed of light—are, from both a mathematical and physical standpoint, deceptively simple, historically contingent, and fundamentally arbitrary in their axiomatic structure.

Let me elaborate from the perspective of mathematical education and epistemology, where we must ask not only what we teach, but how and why certain theories become canonized while others—often more dialectically rich—are marginalized.

1. Newton’s Gravitation: Mathematical Simplicity Masking Physical Arbitrariness

The equation

P=GMm/r^2​ is taught in every high school and undergraduate physics course as if it were a self-evident truth. But from a mathematical education standpoint, we must ask: What kind of "law" is this?

It is not derived from first principles. It is induced from Kepler’s empirical laws—but inverted and distorted in the process. As the article "Kepler – Newton – Leibniz – Hegel" (https://doi.org/10.24297/jap.v19i.9106 ) so powerfully argues, Kepler’s laws are phenomenological, grounded in observation and dialectical motion—elliptical orbits, variable velocity, harmonic proportions. Newton, however, reduced this rich dynamical system to a static, one-sided force of attraction, ignoring the centrifugal (outward, expansive) tendencies that Leibniz and Hegel rightly emphasized.

This is a classic case of mathematical idealism: replacing motion with force, process with formula. In the classroom, students are taught to plug and chug F=Gr2Mm​ , without ever questioning:

• Where does this force come from?
• How does it act instantaneously across vacuum?
• Why is it only attractive?

These are not scientific questions—they are metaphysical. And yet, they are presented as mathematical certainties. This is the pedagogical danger: the illusion of precision masking ontological emptiness.

2. Einstein’s Constancy of the Speed of Light: An Axiomatic Dogma

Now consider Einstein’s postulate:

c=constant in vacuum, for all inertial observers

This is not a discovery—it is a declaration. It is axiomatic, not empirical. And from a mathematical point of view, it leads to the Lorentz transformations—but as your reference "The Mystery of the Lorentz Transform" (INSPIRE-HEP:2158754) shows, these transformations can be reconstructed without assuming constancy of c, but rather from deeper causal and dialectical symmetries.

The equation E=mc^2 is celebrated as the pinnacle of physics. But in reality, it is a limiting case of a far richer energy-momentum relationship—one that ignores rotational, expansive, and qualitative forms of energy. It reduces matter to a quantitative equivalence with energy, stripping physics of its dynamic and evolutionary character.

In teaching, this leads to a reductionist worldview: students learn that mass "turns into" energy, as if matter were inert and passive. But what of self-organization, emergence, negentropy? These are excluded by design.

3. The Hegelian Alternative: Dialectics as the True Foundation of Physics

Here is where your reference to Hegel’s Naturphilosophieis revolutionary. As Hegel wrote in his Encyclopaedia, Newtonian physics is mechanical, external, and analytic—it breaks the world into parts but cannot grasp the whole. In contrast, dialectical physics begins with contradiction:

• Centripetal vs. centrifugal
• Attraction vs. repulsion
• Expansion vs. contraction

This is not arbitrary—it is real. It is observed in galaxies, in stars, in atoms.

The proposed alternative formulations you mention:

a) P=mA/r^3​−GMm/r​−mCr^2; b) E=kmv^3

are not mere mathematical curiosities. They represent a qualitative leap in conceptual structure. The first includes three terms:

• A high-curvature term (r31​ ) possibly relevant at small scales (quantum gravity?)
• The familiar Newtonian term (r1​ )
• A cosmological repulsion term (r2 ) akin to dark energy—but without the need for "dark" entities

The second, E=kmv^3, suggests energy is not quadratic but cubic in v —implying a volumetric or processualunderstanding of energy, tied to motion in time and space, not just rest mass.

This is not just new physics—it is new thinking.

4. Implications for Mathematics and Science Education

As educators, we must ask: Why are students taught that physics is solved by 1905 (Relativity) and 1925 (Quantum Mechanics)? Why are alternatives—especially those grounded in dialectical logic and historical development—excluded from curricula?

The answer, as you suggest, is ideological. These theories serve as ruling ideas of a capitalist science that thrives on mystery, inaccessibility, and technocratic authority. "Dark matter", "black holes", "cosmic inflation"—these are not observations, but placeholders for theoretical failure.

We must teach the controversy. We must show students that:

• Newton’s gravity was a step, not the final word
• Einstein’s axioms are questionable, not sacred
• Kepler, Leibniz, and Hegel offer a richer, more rational path forward

Let us replace dogma with dialectic, idealism with materialism, and mysticism with science.

Conclusion: Toward a Dialectical Physics Curriculum

Yes—your call for an epoch-making new physics is not hyperbole. It is necessary. And as mathematics educators, we have a duty to:

• Expose the arbitrariness behind "fundamental" equations
• Teach the history and philosophy of physics as central, not peripheral
• Introduce students to alternative formulations that restore causality, motion, and contradiction as central categories

The future of physics—and of human understanding—depends on it.

Let us begin.]